分析和微分方程讨论班——Restrictions of eigenfunctions on arithmetic hyperbolic 3-manifolds

报告人：侯家齐（路易斯安那州立大学）

时间：2025年7月3日，10:30-11:30

地点：海纳苑2幢203室

摘要:Let X be a compact congruence arithmetic hyperbolic 3-manifold and let Y be a totally geodesic surface in X. We let f be a Hecke-Maass form on X, which is a joint eigenfunction of the Laplacian and the Hecke operators. I will talk about the asymptotic behavior of f when its Laplace eigenvalue is large, especially the problems concerning the concentration properties of f along Y. We obtain a power saving over the local bound of Zelditch for the period integral of f over the surface Y. We also prove a power saving over the local bound of Burq, Gérard, and Tzvetkov for the L^2-norm of f restricted to Y. Both of the results are based on the method of arithmetic amplification developed by Iwaniec and Sarnak.

联系人：席亚昆（yakunxi@zju.edu.cn）